Conflicts of interest are essentially about relationships. Two persons who are working together happen to have an unknown relationship that influence their work. Companies can find out about these relationships by accident. Someone who is aware of the relationship between the vendor and the employee may step in. This can be a colleague or even a person outside the company. Their motivations can be jealousy, personnal gain or ethical concerns.
Of course, relying only on that kind of accident is a poor company policy for fighting employee/vendors fraud. It is especially true as there are a lot of information sources available to find potentially dangerous connections. Companies have access to emails, social media, news, financial records, purchase orders, employee and vendors lists and a wide range of public databases. Finding conflicts of interest is a matter of mining these information to identify relationships.